An ellipsometer measurement apparatus described in Bosch Technische Berichte, Vol. 4 (1974), No. 7, pages 315–320. It is possible with a measurement apparatus of this kind, for example, to measure the thickness of protective films on aluminum-coated headlight reflectors in the form of a paraboloid mirror with a large aperture ratio; the film thicknesses are in the range from 10 to 50 nm, and a resolution on the order of a nanometer is achievable. For this purpose, a polarized incident beam is directed at a predefined angle of incidence onto a measurement point of the headlight reflector, and is reflected at an angle that is also predefined. The reflected beam is elliptically polarized, and for determination of the ellipticity is conveyed through a rotating analyzer onto a photodetector on which intensity fluctuations of the light signal that correspond to the ellipticity are sensed. The ellipticity and thus the change in intensity depend on the film thickness, so that the latter can be determined in a downstream evaluation device. The angle of the incident beam and reflected beam in terms of the tangential plane or the normal line at the measurement point is often difficult to establish, and accurate adjustment is almost impossible at difficult-to-access locations or with changing curvature profiles, as in the case of modern headlights.